How do I create a star extrusion to circle?
First of all, your Circle should have the same amount of vertices as your Star (or it can have more but then it will be more complicated).

Also you can add Circle in Object Mode and join (Ctrl+J) it with Star or you can just add Circle while being in Star Edit Mode.

Then select both shapes (outer edges) and press CtrlE > Bridge Edge Loops.

After that you will want to select all and Recalculate Normals - CtrlN.